Approximate Stochastic Reachability for High Dimensional Systems
Approximate Stochastic Reachability for High Dimensional Systems
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DOI：
10.23919/acc50511.2021.9483404
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发表时间：
2020-10
期刊：
影响因子：
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通讯作者：
Adam J. Thorpe;Vignesh Sivaramakrishnan;Meeko Oishi
中科院分区：
文献类型：
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作者：
Adam J. Thorpe;Vignesh Sivaramakrishnan;Meeko Oishi
给出了一种计算高维随机动力系统随机能达安全概率的方法。我们的方法利用一种称为条件分布嵌入的非参数学习技术，使用数据驱动的方法对随机核进行建模。通过将动力学和不确定性嵌入到再生核Hilbert空间中，可以用简单的矩阵运算和内积来计算随机可达问题的安全概率。我们使用了一种收敛逼近技术，随机傅立叶特征，以减轻高维系统日益增长的计算要求。这种技术避免了维度灾难，并使高维系统的安全概率计算成为可能，而不需要事先知道动力学或不确定性的结构。我们在一个双积分器系统上验证了该方法，并在百万维、非线性、非高斯、重复平面四旋翼系统上展示了它的能力。
We present a method to compute the stochastic reachability safety probabilities for high-dimensional stochastic dynamical systems. Our approach takes advantage of a nonparametric learning technique known as conditional distribution embeddings to model the stochastic kernel using a data-driven approach. By embedding the dynamics and uncertainty within a reproducing kernel Hilbert space, it becomes possible to compute the safety probabilities for stochastic reachability problems as simple matrix operations and inner products. We employ a convergent approximation technique, random Fourier features, in order to alleviate the increased computational requirements for high-dimensional systems. This technique avoids the curse of dimensionality, and enables the computation of safety probabilities for high-dimensional systems without prior knowledge of the structure of the dynamics or uncertainty. We validate this approach on a double integrator system, and demonstrate its capabilities on a million-dimensional, nonlinear, non-Gaussian, repeated planar quadrotor system.